When you have money earning interest in an account, a decrease in the interest rate costs you money because you no longer receive as much in interest payments. Conversely, if you have an adjustable rate mortgage and rates rise, you lose money because you have to pay more in interest. Calculating how much a change in the interest rate will cost you helps you better budget for your future lower income or higher expenses. To figure the money lost, not only do you need to know the new and old interest rates, but also the amount invested or owed and how long the interest rate change affects your account.
Multiply the number of times interest compounds per year by the number of years over which the changed interest rate applies. For example, if the interest rate fell on your savings account for the next two years and your savings account compounds interest monthly, multiply 2 by 12 to get 24.
Divide the initial interest rate by the number of times per year interest compounds to find the periodic initial interest rate. For example, if you have a 5.61-percent annual interest rate compounded monthly, divide 0.0561 by 12 to get 0.004675.
Add 1 to the original periodic interest rate. In this example, add 1 to 0.004675 to get 1.004675.
Raise the result to the number of compounding periods over which the interest rate change has an effect. Since the interest rate change affects your savings account for 24 compounding periods, raise 1.004675 to the 24th power to get 1.118444127.
Subtract 1 from the answer to find the overall rate of return using the original interest rate. In this example, subtract 1 from 1.118444127 to get 0.118444127.
Repeat Steps 2 through 5 for the new interest rate. In this example, if the savings account interest rate dropped to 4.5 percent, divide 0.045 by 12 to get 0.00375, then add 1 to get 1.00375. Next, raise 1.00375 to the 24th power to get 1.093990118 and subtract 1 to get a total rate of return using the new interest rate of 0.093990118.
Calculate the change in total return by subtracting the total return based on the old interest rate from the total return based on the new interest rate. In this example, subtract 0.118444127 from 0.093990118 to get -0.024454009, meaning the interest you earn decreases, costing you money.
Multiply the change in total return by the amount in the account to calculate your loss based on the change in interest rate. In this example, if you had $10,000 in the savings account, multiply $10,000 by 0.024454009 to find that the change in interest rate for two years will cost you $244.54 in interest.
Based in the Kansas City area, Mike specializes in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."